There has been known a technique of detecting a failure of a filter which is arranged in an exhaust passage of an internal combustion engine for collecting particulate matter (PM) in an exhaust gas, based on a differential pressure between an upstream side and a downstream side of the filter (see, for example, a first patent document). However, it may also be difficult to detect a change in the differential pressure at the time when a failure has occurred in the filter, so there is a fear that the accuracy of failure detection may become low.